I. Field of the Invention
The present relates generally to a method and system for predicting a future position of an automotive vehicle and, more particularly, to such a system utilizing numerical integration of a nonlinear model.
II. Description of Related Art
Many modern automotive vehicles are equipped with some form of vehicle dynamic stability system. Such systems incorporate wheel speed sensors, yaw rate sensors and accelerometers having output signals that are coupled as input signals to a processing unit to control the stability system. Many modern vehicles also include a global positioning system (GPS) receiver to identify the position of the automotive vehicle, typically for a navigation system. Furthermore, current GPS systems of the type used in automotive vehicles typically exhibit an accuracy of one meter or better.
Dedicated short-range communications (DSRC) constitute the leading wireless technology under consideration for cooperative vehicle safety applications. In such systems, automotive vehicles communicate with each other utilizing wireless communications in an effort to increase vehicle safety by decreasing collisions between two or more vehicles. In some systems, an appropriate warning system is provided to the driver of a vehicle warning of an impending collision while, in other systems, the vehicle brakes may be automatically actuated in an attempt to avoid a collision.
In order to achieve crash avoidance between two vehicles, it is necessary to predict the position of the vehicle at a future time within a relatively short time window, typically three to five seconds. Such a relatively short time will enable the operator of the vehicle to apply the brakes, or apply the brakes automatically, in order to avoid the crash.
In order to predict the future position of an automotive vehicle it is conventional to utilize a mathematical nonlinear model of the vehicle. Conventional models include the constant acceleration kinematic model (CA), the kinematic unicycle model (KU), the kinematic bicycle model (KB) or the classic bicycle model (CB). Each model consists of differential equations which, when solved, represent the dynamic action of the automotive vehicle.
Once the model has been selected, the previously utilized approach was to utilize the Kalman Prediction to predict the future horizon position of the vehicle at time T0+Th where Th equals the horizon time offset into the future from the current time T0. Since all of the models are nonlinear, continuous time models, in order to apply the discrete Kalman equations, the nonlinear continuous time models must first be linearized through derivation of the Jacobian state transition matrix and the input gain matrix. In addition, the Kalman Prediction requires that a discrete time system model propagate forward through the prediction horizon Th. Therefore, at each propagation step, Tstep, the linearized, continuous-time system must be discretized as follows:
                    x        ⁡                  (          t          )                            ~                                ∇                      Fx            ⁡                          (              t              )                                      +                  ∇                      Gu            ⁡                          (              t              )                                                                                  ⇓                                                      x        ⁡                  [                      k            +            1                    ]                            =                                            A            d                    ⁢                      x            ⁡                          [              k              ]                                      +                              B            d                    ⁢                      u            ⁡                          [              k              ]                                          where Ad is an n×n matrix, Bd is an n×p matrix, and where Ad and Bd are the discretized system using the sample time Tstep.
While the Kalman Prediction has proven sufficiently accurate in automotive systems for predicting the future position of the vehicle, the Kalman Prediction is necessarily computationally intensive. Since microprocessors of the type used in automotive vehicles, for cost considerations, are not extremely fast, the computational-intensive equations required by the Kalman Prediction mandate relatively long time steps Tstep between sequential equations. This, in turn, can introduce error into the predicted future position of the vehicle.